We have investigated a generic model of non-linearly evolving dynamical dark energy equation of state \(w\) , in the light of the recent Planck, Pantheon, BAO data and recent measurements of \(H_0\)  and \(S_8\) . We have studied the effect of such parameterization on the background and derived cosmological parameters. The results of our analysis is in accordance with the earlier studies with a linear evolution of \(w_{\rm de}\)  (CPL like) [1]}, [2]}, [3]}, [4]} and a few other parameterization of dynamical dark energy [5]}, [6]}, [7]}. We do not get any strong constraints on the two extra parameters \(a_{\rm t}\)  and \(\Delta _{\rm de}\)  at \(\gtrsim 1\sigma \)  level, constraints on \(w_0\)  and \(w_m\)  are in good agreement with the CPL parameterization. In fact this is in good agreement with the [8]} predictions. However, we do get slightly different and a more tightly constrained \(w_0\)  when the model is tested against Planck and external data (Pantheon+BAO) put together. The added external prior on \(M_B\)  and \(S_8\)  makes the difference in CPL and 4pDE parameterization even broader. The 4pDE model can bring down the Hubble tension to \(\sim 2.5 \sigma \)  level and the \(S_8\)  tension to \(\sim 1.5 \sigma \)  level when tested against Planck, BAO and Pantheon supernovae data together. More importantly, we find that there is a negative correlation between parameter \(S_8\)  and \(H_0\)  which is very interesting. However, both the 4pDE model and CPL model improves \(\Delta \chi ^2_{\rm min}\)  for the Planck+Ext data set and the recent measurements of \(H_0\)  and \(S_8\)  in comparison to \(\Lambda \) CDM, this lowering of \(\chi ^2_{\rm min}\)  is achieved at the expense of adding extra parameters. So if we follow \(\Delta \) AIC criteria like recently done by [9]}, the level of success of these models degrades as none of the models has significantly improved \(\Delta \) AIC value over \(\Lambda \) CDM model.
